Method for estimating the state of health of an electrochemical cell for storing electrical energy

ABSTRACT

A method for estimating a state of health of an electrochemical cell for storing electrical energy includes applying at least one current strength peak to the cell, the current peak passing through the cell, measuring a variation, as a function of a time t elapsed after the application of the current peak, of voltage U at the terminals of the cell, and calculating at least one coefficient α I     1    and at least one coefficient U 0,I     1    such that the function √{square root over (t)}→α I     1   ×√{square root over (t)}+U 0,I     1    is a linear approximation of the variation of the voltage U as a function of √{square root over (t)} for √{square root over (t)}≧C, where C&gt;0. The method is used in electrical or hybrid vehicles.

The present invention relates to a method for estimating the state of health of an electrochemical cell for storing electrical energy. It is notably, but not exclusively, applicable to electric or hybrid automobile vehicles.

In the current context of consensus around climate change and global warming, the reduction in emissions of carbon dioxide (CO₂) is a major challenge with which the automobile manufacturers are confronted, the standards being ever more demanding in this regard.

Aside from the continuous improvement in the efficiencies of conventional thermal engines, which is accompanied by a reduction in the emissions of CO₂, electric vehicles (or EVs) and hybrid thermo-electric vehicles (or HEVs) are today considered as the most promising solution for reducing CO₂ emissions.

Various technologies for the storage of electrical energy have been tested in recent years in order to meet the needs of EVs. It turns out today that the batteries using lithium-ion (Li-ion) cells are those that allow the best compromise to be obtained between power density, which favors the performance notably in terms of acceleration, and the energy density, which favors the autonomy.

Unfortunately, the power density and the energy density decrease throughout the lifetime of the battery, notably under the effect of variations in temperature. Thus, after a sufficiently long time of use, an EV may exhibit degraded performance characteristics in terms of autonomy and/or power. This degradation should be controlled in order to maintain sufficient levels of service and of safety.

In order to quantify this degradation, an indicator called “State of Health” (or SOH) has been defined, which is the ratio of the current capacity of a battery with respect to its initial capacity at the beginning of life. Estimating the SOH based on the estimation by impedance measurement of the internal resistance of the battery (or DCR for “Direct Current Resistance”) is known notably from the patent U.S. Pat. No. 6,653,817. Since the internal resistance of a battery characterizes the variation of the voltage U across the terminals of the battery for a certain variation in the intensity I of the current flowing through the battery, the idea of this patent is a precise control of the variation of the intensity I flowing through the battery and a measurement of the variation of the voltage U across the terminals of the battery. One major drawback of this solution is that, if the measurement of voltage is not precise, notably in the case of transient noise signals, the estimation of the resistance may be impacted and the estimation of the SOH may be inaccurate. This is one of the problems to which the present invention aims to provide a solution.

The aim of the invention is notably to solve the aforementioned drawbacks, notably to avoid the measurement problems, by linearizing the measurement of the internal resistance. For this purpose, the subject of the invention is a method for estimating the state of health of an electrochemical cell for storing electrical energy. It comprises a step for applying to the cell at least one current peak of intensity I₁, the current peak flowing through the cell. It also comprises a step for measuring the variation, as a function of the time t that has passed after the application of the current peak, of the voltage U across the terminals of the cell. It also comprises a step for calculating at least one coefficient α_(I) ₁ and at least one coefficient U_(0,I) ₁ such that the function √{square root over (t)}→α_(I) ₁ ×√{square root over (t)}+U_(0,I) ₁ is a linear approximation of the variation of the voltage U as a function of √{square root over (t)} for √{square root over (t)}≧C, where C>0.

In one embodiment, the coefficients α_(I) ₁ and U_(0,I) ₁ may be calculated a first time at the beginning of life of the cell. The method may then comprise a step for calculating the ratio of the value currently calculated of α_(I) ₁ with respect to its value calculated at the beginning of life, where an increase in the coefficient α_(I) ₁ beyond a predetermined value can indicate an incapacity of the cell to deliver a current in its highest ranges of power. The method may also comprise a step for calculating the ratio of the value currently calculated of U_(0,I) ₁ with respect to its value calculated at the beginning of life, where an increase in the coefficient U_(0,I) ₁ beyond a predetermined value can indicate an incapacity of the cell to deliver a current in its highest ranges of power.

In another embodiment, tables or graphs of aging may be filled out beforehand. The method can then comprise a step for comparing the value currently calculated of α_(I) ₁ with values contained in a table or a graph of aging associating levels of aging with values of α_(I) ₁ , in such a manner as to deduce the level of aging of the cell. The method may also comprise a step for comparing the value currently calculated of U_(0,I) ₁ with values contained in a table or a graph of aging associating levels of aging with values of U_(0,I) ₁ , in such a manner as to deduce the level of aging of the cell.

In one preferred embodiment, a plurality of current peaks of intensities (I_(n))_(n≧2) can be applied to the cell (I₁, I₂, I₃, I₄, I₅). The method can then comprise a step for calculating a coefficient β such that the function I→β×I is a linear approximation of the variation of ΔU/√{square root over (t)} as a function of I.

In another embodiment, the coefficient β may be calculated a first time at the beginning of life of the cell. The method may then comprise a step for calculating the ratio of the value currently calculated of β with respect to its value calculated at the beginning of life, where an increase in the coefficient β beyond a predetermined value can indicate an incapacity of the cell to deliver a current in its highest ranges of power.

In another preferred embodiment, tables or graphs of aging may be filled out beforehand. The method may then comprise a step for comparing the value currently calculated of β with values contained in a table or a graph of aging associating levels of aging with values of β, in such a manner as to deduce the level of aging of the cell.

In one preferred embodiment, the method may comprise a step for calculating a coefficient γ such that the function I→γ×I+OCV, where OCV is the open circuit voltage of the cell, is a linear approximation of the variation of U_(0,I) as a function of I.

In one embodiment, the coefficient γ may be calculated a first time at the beginning of life of the cell. The method may then comprise a step for calculating the ratio of the value currently calculated of γ with respect to its value calculated at the beginning of life, where an increase in the coefficient γ beyond a predetermined value can indicate an incapacity of the cell to deliver a current in its highest ranges of power.

In one preferred embodiment, tables or graphs of aging may be filled out beforehand. The method may then comprise a step for comparing the value currently calculated of γ with values contained in a table or a graph of aging associating levels of aging with values of γ, in such a manner as to deduce the level of aging of the cell.

One of the main advantages of the present invention is also that it only requires the software updating of the current devices for estimation of the state of health of a battery.

Other features and advantages of the invention will become apparent with the aid of the description that follows presented with regard to the appended drawings which show:

FIG. 1, with a graph, one example of variation as a function of time t, after application of a current peak of intensity, of the voltage U across the terminals of a Li-ion cell;

FIG. 2, with a graph, the variation of U as a function of √{square root over (t)};

FIG. 3, with a graph, various examples of variation of U as a function of √{square root over (t)} for various current peaks;

FIG. 4, with a graph, the variation of ΔU/√{square root over (t)} as a function of the intensity I;

FIG. 5, with a graph, the variation as a function of I of a coefficient according to the invention;

FIGS. 6, 7, 8 and 9, graphs of aging according to the invention.

The present invention will calculate various coefficients characteristic of the state of health of a Li-ion cell.

As illustrated in the example of FIG. 1, the voltage U across the terminals of a Li-ion cell having a level of charge of the order of 40% can, after a current peak of intensity I₁=74 A (amps) has flowed through this cell at a time t=0, follow a variation from t=0 to t=60 seconds according to the graph illustrated in this figure. Using this simple curve representing the variation of U as a function of time t, it is possible according to the invention to extract various coefficients directly connected to the capacity of the cell to operate at high power density, this capacity being denoted “SOH_(P)” in the following part of the present application, by opposition to its capacity to operate at high energy density which will be denoted “SOH_(E)”.

In the example in FIG. 1, the voltage across the terminals of the cell decreases from 3.86V at t=0 s down to 3.71V at t=60 s in a clearly non-linear manner. The initial voltage value at 3.86V corresponding to the voltage across the terminals of the cell in open circuit, in other words when there is no current flowing through the cell, this voltage being commonly denoted by the acronym OCV for “Open Circuit Voltage”.

FIG. 2 illustrates, as a function of √{square root over (t)} rather than as a function of t, the variation over time of the same voltage U after the current peak of intensity I₁ has flowed through the cell. It is observed that, starting from √{square root over (t)}1, the voltage decreases linearly as a function of √{square root over (t)}, and indeed, one method of linearization shows that the variation of U as a function of √{square root over (t)} may be approximated, for √{square root over (t)}≧1, by the straight line equation U=α_(I) ₁ ×√{square root over (t)}+U_(0,I) ₁ with a slope α_(I) ₁ =−0.011 and with an ordinate at the origin U_(0,I) ₁ =3.7936, these giving a correlation coefficient R²=0.9984.

For a given current I, the slope α_(I) gives information on the SOH_(P) of the cell, notably on its capacity to operate over long periods of time greater than 1 second at a given current.

For a given current I, the ordinate at the origin U_(0,I) also gives information on the SOH_(P) of the cell, in particular:

-   -   the higher U_(0,I) is with respect to the OCV, the less the cell         is capable of operating at high power of the order of 100 to         1000 watts;     -   a high ordinate at the origin U_(0,I) with respect to the OCV         can also indicate that the cell has a problem for short time         periods, in other words at high frequencies, such as connection         hardware or solder joint problems.

Optionally, it is possible to implement a strategy for diagnosing the state of health at several currents according to the present invention, as illustrated in FIGS. 3, 4 and 5 that follow, this strategy allowing a more refined diagnosis.

Indeed, FIG. 3 illustrates, as a function of √{square root over (t)}, the variation over time of the voltage U across the terminals of the same cell having a level of charge of the order of 40%, not only after the current peak of intensity I₁=74 A has flowed through the cell, but also after 4 other peaks with respective intensities I₂=37 A, I₃=18.5 A, I₄=7.4 A and I₅=3.7 A have flowed through this same cell. Here again, irrespective of the peak in question, it is observed that, starting from √{square root over (t)}=1, the voltage decreases linearly as a function of √{square root over (t)}. The same method of linearization shows that the variations of the voltages as a function of √{square root over (t)} may be approximated, for √{square root over (t)}≧1:

-   -   after the peak of intensity I₂, by the straight line equation         U=α_(I) ₂ ×√{square root over (t)}+U_(0,I) ₂ with a slope α_(I)         ₂ =−0.0058 and with an ordinate at the origin U_(0,I) ₂ =3.8268,         these giving a correlation coefficient R²=0.9981;     -   after the peak of intensity I₃, by the straight line equation         U=α_(I) ₃ ×√{square root over (t)}+U_(0,I) ₃ with a slope α_(I)         ₃ =−0.003 and with an ordinate at the origin U_(0,I) ₃ =3.8424,         these giving a correlation coefficient R²=0.9989;     -   after the peak of intensity I₄, by the straight line equation         U=α_(I) ₄ ×√{square root over (t)}+U_(0,I) ₄ with a slope α_(I)         ₄ =−0.0012 and with an ordinate at the origin U_(0,I) ₄ =3.8515,         these giving a correlation coefficient R²=0.9938;     -   after the peak of intensity I₅, by the straight line equation         U=α_(I) ₅ ×√{square root over (t)}+U_(0,I) ₅ with a slope α_(I)         ₅ =−0.0007 and with an ordinate at the origin U_(0,I) ₅ =3.8546,         these giving a correlation coefficient R²=0.9652.

On the one hand, FIG. 4 illustrates the variation over time of ΔU/√{square root over (t)} as a function of the intensity I, for the values I₁=74 A, I₂=37 A, I₃=18.5 A, I₄=7.4 A and I₅=3.7 A in FIG. 3. It is observed that ΔU/√{square root over (t)} decreases linearly with I, and indeed, one method of linearization shows that the variation of ΔU/√{square root over (t)} as a function of I may be approximated by the straight line equation ΔU/√{square root over (t)}=β×I with a slope β=−0.000151 and with an ordinate of zero at the origin, these giving a correlation coefficient R²=0.998.

The slope β reveals the sensitivity of the cell to the current over long time constants, in other words diffusion phenomena. The slope β indicates the capacity of the cell to operate at high currents: the higher the absolute value of the slope β, the more the cell is sensitive to the use of high currents.

On the other hand, FIG. 5 illustrates the variation over time of the ordinate at the origin U_(0,I) of the curves illustrated in FIG. 3, as a function of the intensity I, for the values I₁=74 A, I₂=37 A, I₃=18.5 A, I₄=7.4 A and I₅=3.7 A in FIG. 3. It is observed that U_(0,I) decreases linearly with I, and indeed, one method of linearization shows that the variation of U_(0,I) as a function of I may be approximated by the straight line equation U_(0,I)=γ×I+OCV with a slope γ=−0.000868 and with an ordinate at the origin OCV=3.86, these giving a correlation coefficient R²=1. As regards the slope γ, this corresponds to the internal resistance of the cell, which is therefore equal to 0.868 milliOhms (mΩ) at this level of charge of 40% and which corresponds to an impedance measured at 3.5 Hertz (Hz).

Since it corresponds to the internal resistance of the cell, the slope γ therefore also provides information on the SOH_(P) of the cell: the steeper the slope γ, the more the SOH_(P) of the cell is degraded. In a more precise manner than the ordinate at the origin U_(0,I) as a function of the intensity I, the slope γ estimated using the U_(0,I) values provides information on the capacity of the cell to operate over short times, in other words at high frequencies. It provides information on the resistance of the cell at high frequencies which, if it is high, may be explained by a problem of connection hardware or of significant aging of the cell.

In the latter case, the coefficients α₁ and β should indicate aging. Hence, if the coefficients α₁ and β are acceptable and if the coefficient γ is not, it may be deduced that the problem at high frequencies is due to a problem of connection hardware.

Once the coefficients α₁, β, U_(0,I) and γ have been calculated according to the present invention, they may be used in various ways.

As previously described, a first way is to use them for the purposes of diagnosing the cell, in order to notably estimate its capacity to operate at high power, in other words to estimate its SOH_(P), or even to diagnose a fault in connection hardware. For example, for α₁, β and γ, a ratio may be calculated between the value calculated at the current time and the value initially calculated, namely α_(I,BOL), β_(BOL) and γ_(BOL) respectively, where the abbreviation “BOL” denotes “Beginning Of Life”. The relative variation of the ratios α₁/α_(I,BOL), β/β_(BOL) et γ/γ_(BOL) over time may thus be observed: if a coefficient at a given moment is increasing too much with respect to its initial value, whereas the other coefficients show the expected variation over time, then the cell most probably has a connection hardware fault. It is also possible to observe ratios of the type γ/β or γ/α_(I). In the example illustrated in the figures, during the life of the cell, the ratio γ/β varies between 4.59 and 5.78. However, a connection hardware fault of 0.2 mΩ makes this variation go between 5.78 and 6.814, whereas a fault of 1 mΩ makes this variation go between 10.56 and 11.17. By making a prior estimation of these various values, it is possible to detect connection hardware problems at the beginning of life and during the life of the cell.

Another way of using them is to estimate the SOH_(E) of the cell using tables or graphs of aging, such as the graphs illustrated in FIGS. 6, 7, 8 and 9 for the slope α_(I), the slope β, the ordinate at the origin U_(0,I) and the slope γ, respectively. These graphs associate, with values of said coefficients, values in arbitrary units (a.u.), these values in arbitrary units characterizing the aging of a cell. For example, a value 0 on the abscissa characterizes the beginning of the life of the cell and a value 9 characterizes the end of the life of the cell. These graphs are filled out prior to using the cell, during campaigns for studying the process of aging of the cells throughout their life. Thus, according to FIG. 6, the slope α_(I) increases from substantially 0.0062 at the beginning of life of the cell up to substantially 0.0076 at the end of life of the cell. According to FIG. 7, the slope β increases from substantially 0.000163 at the beginning of life of the cell up to substantially 0.000194 at the end of life of the cell. According to FIG. 8, the ordinate at the origin U_(0,I) increases from substantially 3.829 at the beginning of life of the cell up to substantially 3.848 at the end of life of the cell. Finally, according to FIG. 9, the slope γ firstly decreases from substantially 0.00082 to substantially 0.00077 at the beginning of life of the cell, before increasing up to substantially 0.00112 at the end of life of the cell.

Another way of using the coefficients α_(I), β, U_(0,I) and γ calculated according to the present invention is to compare one cell with another in a module or a pack comprising several cells, or else in such a manner as to compare the variation over time of various types of cells in the case of cells based on different chemistries or not coming from the same supplier.

The invention described hereinabove has the further main advantage that, since it only requires a software updating of the current devices for estimating the state of health, its cost of implementation is very low. 

1. A method for estimating the state of health of an electrochemical cell for storing electrical energy, the method comprising: applying to the cell at least one current peak of intensity I₁, the current peak flowing through the cell; measuring the variation, as a function of the time t that has passed after the application of the current peak, of the voltage U across the terminals of the cell; and calculating at least one coefficient α_(I) ₁ and at least one coefficient U_(0,I) ₁ such that the function √{square root over (t)}→α_(I) ₁ ×√{square root over (t)}+U_(0,I) ₁ is a linear approximation of the variation of the voltage U as a function of √{square root over (t)} for √{square root over (t)}≧C, where C>0.
 2. The method as claimed in claim 1, wherein, the coefficients α_(I) ₁ and U_(0,I) ₁ having been calculated a first time at the beginning of life of the cell, the method further comprises: calculating the ratio of the value currently calculated of α_(I) ₁ with respect to its value calculated at the beginning of life, an increase of the coefficient α_(I) ₁ beyond a predetermined value of said ratio indicating an incapacity of the cell to deliver a current in its highest ranges of power, and/or; calculating the ratio of the value currently calculated of U_(0,I) ₁ with respect to its value calculated at the beginning of life, an increase in the coefficient U_(0,I) ₁ beyond a predetermined value of said ratio indicating an incapacity of the cell to deliver a current in its highest ranges of power.
 3. The method as claimed in claim 1, wherein, tables or graphs of aging having been filled out beforehand, the method further comprises: comparing the value currently calculated of α_(I) ₁ with values contained in a table or a graph of aging associating levels of aging with values of α_(I) ₁ , in such a manner as to deduce the level of aging of the cell, and/or; comparing the value currently calculated of U_(0,I) ₁ with values contained in a table or a graph of aging associating levels of aging with values of U_(0,I) ₁ , in such a manner as to deduce the level of aging of the cell.
 4. The method as claimed in claim 1, wherein, a plurality of current peaks of intensities (I_(n))_(n≧2) being applied to the cell (I₁, 1 ₂, I₃, I₄, I₅), the method further comprises: calculating a coefficient β such that the function I→β×I is a linear approximation of the variation of ΔU/√{square root over (t)} as a function of I.
 5. The method as claimed in claim 4, wherein, the coefficient β having been calculated a first time at the beginning of life of the cell, the method further comprises: calculating the ratio of the value currently calculated of β with respect to its value calculated at the beginning of life, an increase in the coefficient β beyond a predetermined value of said ratio indicating an incapacity of the cell to deliver a current in its highest ranges of power.
 6. The method as claimed in claim 4, wherein, tables or graphs of aging having been filled out beforehand, the method further comprises: comparing the value currently calculated of β with values contained in a table or a graph of aging associating levels of aging with values of β, in such a manner as to deduce the level of aging of the cell.
 7. The method as claimed in claim 4, further comprising: calculating a coefficient γ such that the function I→γ×I+OCV, where OCV is the open circuit voltage of the cell, is a linear approximation of the variation of U_(0,I) as a function of I.
 8. The method as claimed in claim 7, wherein, the coefficient γ having been calculated a first time at the beginning of life of the cell, the further method comprises: calculating the ratio of the value currently calculated of γ with respect to its value calculated at the beginning of life, an increase in the coefficient γ beyond a predetermined value of said ratio indicating an incapacity of the cell to deliver a current in its highest ranges of power.
 9. The method as claimed in claim 8, wherein, tables or graphs of aging having been filled out beforehand, the method further comprises: comparing the value currently calculated of γ with values contained in a table or a graph of aging associating levels of aging with values of γ, in such a manner as to deduce the level of aging of the cell. 